0=-4n^2+64n-112

Solution for 0=-4n^2+64n-112 equation:

Simplifying
0 = -4n2 + 64n + -112

Reorder the terms:
0 = -112 + 64n + -4n2

Solving
0 = -112 + 64n + -4n2

Solving for variable 'n'.

Combine like terms: 0 + 112 = 112
112 + -64n + 4n2 = -112 + 64n + -4n2 + 112 + -64n + 4n2

Reorder the terms:
112 + -64n + 4n2 = -112 + 112 + 64n + -64n + -4n2 + 4n2

Combine like terms: -112 + 112 = 0
112 + -64n + 4n2 = 0 + 64n + -64n + -4n2 + 4n2
112 + -64n + 4n2 = 64n + -64n + -4n2 + 4n2

Combine like terms: 64n + -64n = 0
112 + -64n + 4n2 = 0 + -4n2 + 4n2
112 + -64n + 4n2 = -4n2 + 4n2

Combine like terms: -4n2 + 4n2 = 0
112 + -64n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(28 + -16n + n2) = 0

Factor a trinomial.
4((2 + -1n)(14 + -1n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Subproblem 2
Set the factor '(14 + -1n)' equal to zero and attempt to solve:

Simplifying
14 + -1n = 0

Solving
14 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-14' to each side of the equation.
14 + -14 + -1n = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1n = 0 + -14
-1n = 0 + -14

Combine like terms: 0 + -14 = -14
-1n = -14

Divide each side by '-1'.
n = 14

Simplifying
n = 14
Solution
n = {2, 14}